. Dominated and Iteratively Dominated Strategies. Consider the oligopoly model we discussed in class with I = 2 competitors and linear demand and cost functions: p (q) = a bq; ci (qi) = c qi and the aggregate supply is: q = q1 + q2. In class, we deÖned a dominant and a dominated strategy. Now we try to apply the notion of domination repeatedly and iteratively. (a) Thus suppose that each Örm i is initally considering a quantity: qi 2 R+, and now suppose that each Örm is eliminating all strategies, supply choices, that are strictly dominated by some other choices, and call the remaining set of undominated strategies U 1 i R+. Graphically describe the remaining set U i 1 of action/strategies for Örm i = 1; 2. (b) We can then reÖne and iterate the analysis by asking which strategies are dominated for Örm i if Örm j is know to only choose actions from U 1 j , and call the remaining strategies U 2 i . Graphically describe the remaining set of action/strategies for Örm i = 1; 2. What do you observe? (c) If we iterate the analysis for every k, then we can ask what is limit set of strategies that survives the iterative process of eliminating dominated strategies. Can you desribe lim k!1 U k i :

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